What is the product of #5 (cos frac{3\pi}{4}+isinfrac{3\pi}{4} ) \cdot \sqrt{3}(cosfrac{\pi}{2}+i sinfrac{\pi}{2})#?

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Answer 1 · 2018-06-14T04:37:02

#color(maroon)(=> -5sqrt(3/2) + i 5sqrt(3/2)# or #-5sqrt(3/2)(1-i)#

#Z_1 * Z_2 = r_1*r_2 (cos (theta_1+ theta_2) + i sin (theta_1 + theta_2))#

#Z_1 = 5 (cos ((3pi)/4) + i sin ((3pi)/4)#

#Z_2 = sqrt3 (cos (pi/2) + i sin (pi/2))#

#r_1 =5, r_2 = sqrt3, theta_1 = (3pi)/4, theta_2 = pi/2#

#Z_1 * Z_2 = 5 sqrt3 ((cos ((3pi)/4 + pi/2) + i sin ((3pi)/4 + pi/2))#

#=> 5 sqrt3 * (-(1/sqrt2) + i (1/sqrt2))#

#color(maroon)(=> -5sqrt(3/2) + i 5sqrt(3/2)# or #-5sqrt(3/2)(1-i)#